Full text of DOI:10.1111/j.1151-2916.2000.tb01678.x

J. Am. Ceram. Soc., 83 [12] 3025–32 (2000)
journal
High-Temperature Mechanical Properties of
Si-B-C-N-Precursor-Derived Amorphous Ceramics and the
Applicability of Deformation Models Developed for Metallic Glasses
Martin Christ, G u¨ nter Thurn, Markus Weinmann, Joachim Bill, and Fritz Aldinger*
Max-Planck-Institut f u¨ r Metallforschung and Institut f u¨ r Nichtmetallische Anorganische Materialien,
Universit a¨ t Stuttgart, Pulvermetallurgisches Laboratorium, Heisenbergstrasse 5, 70569 Stuttgart, Germany
The characterization of Si-B-C-N amorphous ceramics using
isothermal compression creep testing in the temperature range
of 1200°–1500°C is reported. The deformation rate contains a
stress-dependent component that is proportional to the applied
stress, which indicates that this portion of the deformation
mechanism is based on viscous flow. An increase in the creep
resistance is observed, following either preliminary annealing
or hot isostatic pressing, which may be explained by a reduc-
tion of free volume in the amorphous material. The application
of two deformation models that are used to predict similar
deformation behavior in metallic glasses also is discussed.
Although both models accurately predict the time dependence
of the deformation rate of precursor-derived amorphous ce-
ramics, the free-volume model fits the observed temperature
dependence better than the “two-step” rearrangement model.
silazanes—with chemical compositions of (B[C H –Si(CH )NH] )
2 4 3 3 n
15
(denoted hereafter as T2-1) and (B[C H –Si(H)NH] ) (denoted
2
4
3 n
5
hereafter as MW33) —were investigated. Details of the synthesis
5
,15
for both polymers have been presented elsewhere.
Both poly-
mers are brittle and unmeltable products that can be pulverized
using a vibrating-disk mill. For compaction, sieved polymer
powders were heated in a graphite die to a temperature where the
polymers softened but did not melt (150°–350°C) and then
densified at an applied pressure of 48 MPa. The obtained green
bodies were converted to amorphous ceramic monoliths via
thermolysis in an argon atmosphere at a temperature of 1400°C
for 2 h. The chemical compositions of the T2-1- and MW33-
1
5
derived ceramics were determined to be Si B1.0C4.3N2.0 and
3
5
Si B1.1C5.3N3.0
, respectively. After the plastic-forming condi-
3
tions were optimized, the final ceramic monoliths had a total
porosity of ϳ15%. Because of the hardness of the MW33 polymer
powder, the resulting ceramic exhibited only open porosity,
whereas approximately one-third of the porosity in the T2-1-
derived ceramic was closed. After thermolysis, some samples were
annealed in a nitrogen-gas atmosphere at 1400°C for 80 h or
encapsulated in quartz glass and hot isostatically pressed (HIPed)
at 1600°C and 200 MPa for 4 h.
I. Introduction
HE thermolysis of organometallic polymers offers a promising
T
processing route for the fabrication of ceramics for high-
1,2
temperature use. Materials in the Si-B-C-N system began to
attract interest within the past decade, because they possess
1
,3,4
After thermolysis (and, for some batches, subsequent heat or
pressure treatment), creep specimens with a height of 3 mm and a
cross-sectional area of 1.8 mm ϫ 1.8 mm were cut from the
ceramic monoliths and ground. The high-temperature mechanical
properties were investigated using compression creep testing in air
at 1200°–1500°C and applied stresses in the range of 5–300 MPa.
The mechanical testing equipment and procedure have been
excellent stability
tures.
and oxidation resistance at high tempera-
5
The absence of low-melting-point grain-boundary phases in
precursor-derived materials leads to extraordinary high-
temperature mechanical properties, which are very different from
those of conventionally sintered materials. In recent studies of the
6
,7
high-temperature mechanical properties of as-thermolyzed Si-C-N
and Si-B-C-N
6
8
–10
described elsewhere.
materials, the amorphous state revealed out-
The open and closed porosities were calculated from the
measured density of the ceramic monoliths and the amorphous
matrix, using the following procedure. The bulk density was
calculated from displacement measurements in mercury. The
volume of the ceramic matrix, including the closed pores, was
measured using a helium-gas pycnometer (Model Accupyc 1300,
Micromeritics Instruments Group, Norcross, GA). The density of
the ceramic matrix was determined via helium-gas pycnometry,
using fine crushed ceramic powder particles (Ͻ32 ␮m in size) that
were assumed to contain no closed porosity. Using these three
measurements, the volume fraction of the ceramic matrix can be
obtained and the open and closed porosities can be calculated.
standing mechanical stability at rather-high temperatures, although
the deformation mechanisms are not yet well understood. The
objective of this paper is to report on compression tests of
Si-B-C-N-precursor-derived ceramics and give a more-detailed
analysis of the deformation mechanisms. As will be shown, some
characteristic features of the deformation behavior of precursor-
derived amorphous ceramics are similar to those observed in
metallic glasses that have been under investigation for several
1
1–14
decades.
Therefore, the applicability of two of the deforma-
tion models that have been developed for metallic glasses will be
discussed for precursor-derived amorphous ceramics.
II. Experimental Procedures
III. Results
The high-temperature mechanical properties of Si-B-C-N ce-
ramics that were derived from two boron-modified poly(vinyl)
(
1) Comparison of T2-1- and MW33-derived Ceramics
The ceramic materials that were obtained from both boron-
modified polysilazanes exhibited similar mechanical properties.
The two compounds had similar compositions and were processed
under equivalent conditions. The resulting porosity was ϳ15% in
both materials. Figure 1 shows a log–log plot of the time
dependence of the deformation rates for both materials during a
long-term creep experiment at a pressure of 100 MPa. The figure
shows that the evolution of the deformation rate is similar for both
S. M. Wiederhorn—contributing editor
Manuscript No. 189045. Received October 1, 1999; approved June 15, 2000.
*Member, American Ceramic Society.
3
025

3
026
Journal of the American Ceramic Society—Christ et al.
Vol. 83, No. 12
in conventional materials, which often are described using the
Norton power law, which is given in Eq. (1):
ϪQ
n
Ϫc
⑀
˙ ϭ A␴ expͩ ͪ
t
(1)
RT
where ␴ is the applied stress, n the stress exponent, Q the
activation energy, R the gas constant, T the absolute temperature,
t the time, and c the time exponent. A is a constant. The absolute
value of the slope of the curve in Fig. 2 increases with time: the
5
time exponent increases from c Ϸ 0.66 at t Ͻ 10 s (range I) to c Ϸ
5
1
for t Ͼ 2 ϫ 10 s (range II). It will be shown later that this
change in c does not necessarily translate to a change in the real
time dependence of ⑀˙ . For this reason, c will be called the apparent
time exponent. Figure 2 shows that the development of ⑀˙ is not
dependent on ␴.
(3) Temperature Dependence of Deformation
Fig. 1. Comparison of the deformation rates of MW33- and T2-1-derived
amorphous ceramics during isothermal creep testing.
The influence of temperature T on the deformation rate ⑀˙ of
T2-1-derived ceramics is shown in Fig. 3. All the experiments
were performed at a compressive stress of 50 MPa. The time
dependence is qualitatively the same for all the temperatures. All
the curves show an increase in c; however, the transition from
range I to range II occurs earlier at elevated temperatures.
Although the apparent time constant changes to a value of c Ϸ 1
Si-B-C-N materials. The deformation rates for the MW33- and
T2-1-derived materials decrease from starting values of ⑀˙ Ϸ 6 ϫ
Ϫ7
Ϫ7 Ϫ1
Ϫ8 Ϫ1
6
1
0
and 9 ϫ 10
s
, respectively, to ⑀˙ Ͻ 10
s
after 10
5
5
after 5 ϫ 10 s at 1350°C, this transition occurs after 3 ϫ 10 s at
5
s. Up to a time of t ϭ 10 s, the two curves are somewhat parallel;
for t Ͼ 10 s, the curves overlap. The error bars for the
4
4
1
400°C, after 5 ϫ 10 s at 1450°C, and after 2 ϫ 10 s at 1500°C.
5
No temperature influence on c could be detected in either range I
or II.
deformation rates in Fig. 1 are within the size of the symbols and
have been omitted for clarity.
The typical total deformation achieved at 1400°C in a 100 h
creep test is ϳ2%–5%; this value is dependent on the applied
stress but is independent of the type of material. For the following
analysis, the elastic deformation is not considered.
In range I (c Ϸ 0.66), ⑀˙ increases as T increases. The curves are
parallel in this range; therefore, the activation energy Q can be
calculated according to Eq. (1). By plotting the logarithm of ⑀˙ after
a testing time of 3000 s versus the reciprocal temperature 1/T (see
Fig. 4), the activation energy in the temperature range of 1200°C–
1
500°C is determined to be Q ϭ 0.23 Ϯ 0.04 MJ/mol. The error
(
2) Time Dependence of Deformation
Figure 2 presents a detailed analysis of the time dependence of
is the statistical error of the fitted line shown in Fig. 4. For range
II, the apparent time exponent is independent of temperature (c Ϸ
1), as in range I; however, in contrast to range I, ⑀˙ is independent
of T.
The curves in Fig. 3 are not equidistant for all times; therefore,
the above-determined activation energy Q is not attributed to a
simply thermally activated process. There are several possible
reasons for this behavior. One possibility is that the transition from
range I to range II is caused by a change between two deformation
the deformation rate of T2-1-derived material under different
applied stresses at a temperature of 1400°C. This type of time
dependence has been observed in both Si-C-N and Si-B-C-N
amorphous ceramics. The deformation rate decreases as the time
increases, and even after 450 h, no stationary creep is observed. In
other words, the creep resistance of the material is improved
during the creep test. This decrease in ⑀˙ is similar to primary creep
6
,9
Fig. 2. Variation of the deformation rates, relative to time and applied compressive stress, during isothermal creep experiments with T2-1-derived
amorphous ceramics at 1400°C.

December 2000
High-Temperature Mechanical Properties of Si-B-C-N-Precursor-Derived Amorphous Ceramics
3027
Fig. 3. Variation of the deformation rate, relative to time, at 50 MPa and different temperatures during isothermal creep experiments with T2-1-derived
amorphous ceramics.
Fig. 4. Arrhenius plot for the calculation of the apparent activation
energy of the deformation rate of T2-1-derived material after 3000 s. All
tests were performed at a stress of 50 MPa. Error given is the statistical
error of the linear curvefitting.
Fig. 5. Stress dependence of the normalized deformation rate ( ⑀˙ ϫ
Ϫ4 Ϫ0.66
10 /t
) of the T2-1-derived amorphous ceramic at 1400°C in time
5
range I (t Ͻ 10 s).
6
ceramics. The stress-dependent component of the deformation has
mechanisms with different activation energies. Another possibility
is that the relationship between ⑀˙ and Q is not Arrhenius-like.
Therefore, the activation energy when determined in this manner
will be called the apparent activation energy.
a linear relation with ␴ (i.e., a stress exponent of n ϭ 1).
Based on the previous arguments, the dependence of ⑀˙ on t and
␴ can be described empirically, according to the following
equation:
n
Ϫc
␴
t
(
4) Stress Dependence of Deformation
As mentioned previously, the time dependence of the deforma-
⑀
˙ ϭ
ͫ
⑀˙ 0 ϩ ⑀˙ 1ͩ ͪ ͬͩ ͪ
(3)
␴
t
0
0
tion rate is independent of the applied stress ␴. This condition is
fulfilled by the following relationship:
where ⑀˙ and ⑀˙ are constants. To obtain dimensionless values, the
applied stress and time are normalized by ␴ and t , respectively.
0
1
0
0
In range I, the data fit well for n Ϸ 1 and c Ϸ 0.66. Analogously,
the stress-dependent deformation in range II also was analyzed.
Figure 6 shows that Eq. (3) also describes the deformation
behavior in this range for n Ϸ 1 and c Ϸ 1, using different values
for ⑀˙ and ⑀˙ .
Although Eq. (3) is a good fit to the measured deformation rate,
one must note that it is only an empirical approximation. It is not
based on any assumptions that have been made on the deformation
mechanism; instead, it has been developed in analogy to the
Norton power law (Eq. (1)) and modified by a stress-independent
component of the deformation rate.
⑀
˙͑␴,t͒ ϭ g͑␴͒ f͑t͒
(2)
Ϫc
For this case of f(t) (where f(t) ϰ t ), there are different values of
c for range I and range II. According to Eq. (2), the stress-
dependency term (g(␴)) can be separated by dividing the defor-
mation rate ( ⑀˙ ) by the time-dependent term (f(t)).
The dependence of the normalized deformation rate of T2-1-
derived material on ␴ at a temperature of 1400°C in range I is
shown in Fig. 5. A deformation intercept also occurs if the
specimen is not loaded; this effect can be ascribed to shrinkage.
Similar shrinkage has been observed in Si-C-N-precursor-derived
0
1

3
028
Journal of the American Ceramic Society—Christ et al.
Vol. 83, No. 12
3
density of the as-thermolyzed material (2.40 g/cm ). The differ-
ence in the density between amorphous and crystalline material of
the same chemical composition is considered to be due to the free
volume in the amorphous state, i.e., the distortion of the amor-
phous state, with respect to the long-range-ordered, dense crystal-
line solid. Using values obtained from helium-gas pycnometry, the
free volume in the as-thermolyzed state (Vf, therm) is assessed to be
ϳ14%. Analogously, the free volume of the annealed sample
(
(
Vf, ann) is determined to be ϳ12% and that of the HIPed sample
Vf, HIP) is ϳ8.6%. No significant changes are observed in the
porosity after annealing or HIP. No crystallization can be detected
using X-ray diffractometry (XRD) (see Fig. 8), and only a very
small amount of nanocrystalline phases (ϽϽ10 vol%) can be
1
6
observed via transmission electron microscopy (TEM); there-
fore, the decrease of the free volume likely causes the improve-
ment in the creep resistance. This result will be the main topic of
discussion in section IV.
Fig. 6. Stress dependence of the normalized deformation rate ( ⑀˙ ϫ
Ϫ2 Ϫ1
(
6) Oxidation
1
0 /t ) of the T2-1-derived amorphous ceramic at 1400°C in time range
5
II (t Ͼ 2 ϫ 10 s).
With respect to practical use of the material, the oxidation
behavior is of interest. Therefore, all creep tests that have been
presented here were performed in air, and the tested samples were
characterized with respect to oxidation.
(5) Influence of Matrix Density
The duration of the creep experiments at 1400°C was 90–450
h. Generally, the oxidation behaviors of both materials that were
investigated were similar. Scanning electron microscopy (SEM)
analysis indicated the presence of a passivating oxide layer on the
surface of all creep specimens that were tested at 1400°C; the
thickness of this layer was ϳ30 ␮m. No dependence on the
duration of the creep experiment could be determined.
The density of the pore-free ceramic matrix of precursor-
derived ceramics can be increased by annealing or by HIP. No
significant changes in the sample composition have been observed
during annealing or HIP, according to energy-dispersive X-ray
spectroscopy (EDX).
The density of the as-thermolyzed compounds (␳
) was 2.35
therm
3
3
g/cm for the T2-1-derived ceramic matrix and 2.40 g/cm for the
MW33-derived ceramic matrix. Heat treatment of the MW33-
derived ceramic matrix at a temperature of 1400°C in a nitrogen-
gas atmosphere for 80 h increased the pore-free density (␳ann) to
A large portion of the porosity was open; therefore, the pores
also contained oxide layers. The thickness of these layers was ϳ2
␮m for all the samples that were investigated. The oxygen content
3
of the ceramic matrix, as measured via EDX, decreased rapidly as
the distance from the interface between the oxide layer and the
matrix phase increased. After a distance of Ͻ5 ␮m, the oxide
content approached that which was measured in the chemical
analysis of the as-thermolyzed material.
ϳ2.47 g/cm . A similar increase in the pore-free density of the
MW33-derived ceramic matrix was observed after HIPing at
1
(
600°C and 200 MPa for 4 h, which resulted in a post-HIP density
3
␳HIP) of ϳ2.56 g/cm . The porosity of the samples after both
treatments remained almost constant. An overview of this data is
given in Table I.
Porosimetry investigations of oxidized samples (see Fig. 9)
show an increase in the closed porosity during annealing in air at
The increase in the density of the ceramic matrix led to an
improvement of the high-temperature mechanical properties of the
MW33-derived material. Figure 7 shows the time dependency of
the deformation rate of a sample after thermolysis, annealing, and
HIP. The samples that have an increased matrix density are more
resistant to creep than samples that have a lower matrix density.
The slope of the time dependence of the deformation rate is the
same for all three samples and, therefore, is independent of matrix
density and thermal pre-treatment. This observation indicates that
the change in c is not due to a temperature-induced change in the
microstructure of the material, because such action would cause
the change in c for the annealed material to shift to shorter times.
In thermodynamic equilibrium, a MW33-derived crystalline
ceramic should consist of 21.7 wt% graphite (density of ␳ ϭ 2.25
1
400°C. The total porosity of the samples before the heat treatment
was ϳ20%. Because of the formation of oxide layers inside the
pores, the total porosity was reduced to ϳ15%. The volume of
closed porosity in the as-thermolyzed state was ϳ2%, which
increased during the oxidation test to a saturation value of 11%
after 10 h.
IV. Discussion
(1) Time Dependence of the Deformation Rate
As shown previously, the deformation of precursor-derived
ceramics consists of two components: a stress-independent term
that is ascribed to shrinkage and a stress-dependent term. All the
data points in Fig. 5 lie on a straight line; therefore, this component
of the deformation is linear with the applied stress ␴ and, thus, is
Newtonian in range I. According to this plot, Eq. (3) was proposed
as an approximation for the dependence of the deformation rate on
time and stress at 1400°C. Because this observation also is valid in
range II, this result leads to the assumption that the stress-
dependent portion of the deformation mechanism is based on
viscous flow. Therefore, the viscosity ␩ can be calculated using the
relation
3
3
g/cm ), 32.5 wt% Si N (␳ ϭ 3.20 g/cm ), 14.0 wt% BN (␳ ϭ 2.27
3
4
3
3 5
g/cm ), and 31.8 wt% SiC (␳ ϭ 3.20 g/cm ). Using the rule of
mixtures, the calculated density of a crystalline material with this
3
composition would be 2.8 g/cm , in comparison with the measured
Table I. Influence of Annealing and Hot Isostatic Pressing
HIP) on the Free Volume and Porosity of MW33-derived
(
Amorphous Material
Powder density
Total porosity
(%)
Free volume
(%)
3
Conditions
(g/cm )
␶
1
3
␴
␩
ϭ
ϭ
ͩ ͪ
(4)
␥˙
⑀˙
New
After thermolysis
2.40
2.47
2.56
15
16
13
14
12
8.6
‡
†
After annealing
‡
where ⑀˙ New is the Newtonian component of the deformation rate.
The Newtonian component was separated from the total deforma-
tion rate by the following process. Figure 5 shows that the
deformation rate measured at an applied load of 5 MPa is a good
After HIP
†
Annealing conditions were 1400°C for 80 h in a nitrogen-gas atmosphere. HIP
conditions were 1600°C for 4 h at 200 MPa, and the sample was encapsulated in
quartz glass.

December 2000
High-Temperature Mechanical Properties of Si-B-C-N-Precursor-Derived Amorphous Ceramics
3029
Fig. 7. Time dependence of the deformation rate of amorphous as-thermolyzed, post-annealed, and post-HIPed MW33-derived ceramics. All tests were
performed at 1400°C and 100 MPa. Powder densities, porosities, and free volumes are listed in Table I.
Fig. 8. XRD patterns of MW33-derived samples (as-thermolyzed, an-
nealed (1400°C for 80 h in a nitrogen-gas atmosphere), and HIPed (1600°C
and 200 MPa for 4 h, encapsulated in quartz glass)).
Fig. 9. Closure of open pores with time during annealing in air at
1
400°C; the total porosity of the sample was ϳ20%. Inset shows a SEM
micrograph of the fracture surface of a specimen after creep testing for
50 h in air; the thickness of the oxide layer (bright region) inside the pore
4
approximation for the shrinkage rate. Consequently, the Newto-
is typical for creep specimens after testing for a duration of Ͼ90 h.
nian component of the deformation rate at stress ␴ and time t
(
⑀˙ New(␴,t)) was calculated from the measured total deformation
The line that is plotted in Fig. 10 shows a least-mean-square
error fit of the viscosity data to the function ␩(t) ϭ a ϩ bt, which
is the simplest linear time dependence. The good correspondence
of the measured data with the fit data shows that ␩ increases
rate ⑀˙ total(␴,t) by subtracting the deformation rate that has been
measured at quasi-negligible stress ( ⑀˙ total(5 MPa,t)):
⑀
˙
New͑␴,t͒ ϭ ⑀˙ total͑␴,t͒ Ϫ ⑀˙ total͑5 MPa,t͒
(5)
linearly as t increases. This feature also is characteristic of other
Figure 10 shows the time dependence of the viscosity that has
been calculated using Eqs. (4) and (5) for the T2-1-derived ceramic
at a temperature of 1400°C at various applied stresses. Although ␩
12,14,18–21
amorphous materials, e.g., metallic glasses.
Other fea-
tures that are observed in both metallic glasses and precursor-
derived amorphous ceramics include Newtonian flow at low
stresses, the occurrence of shrinkage during annealing, and a
strong influence of a preliminary heat treatment on the kinetics of
creep. Therefore, it is concluded that the deformations of metallic
glasses and precursor-derived amorphous ceramics are based on
similar mechanisms.
is independent of ␴, it changes by two orders of magnitude, within
6
1
0 s. This tremendous increase cannot be explained by crystalli-
zation. According to TEM investigations, the amount of crystalline
phases in the material that has been investigated in this work after
1
6
a heat treatment at 1400°C for 80 h is ϽϽ10%. Also, after HIP,
no crystallization can be detected via the XRD analysis in Fig. 8.
According to Einstein’s equation for the flow of partly crystalline
For metallic glasses, several deformation mechanisms have
11,14,19–22
been discussed in the literature.
Two of them, which
1
7
mixtures,
predict a linear increase of the viscosity with time, will be
1
4,22
discussed here. One theory
explains the deformation of me-
␩eff ϭ ␩͑1 ϩ 2.5␰͒
(6)
tallic glasses by structural relaxation of the material via noncorre-
lated, two-stage, elementary-shear atomic rearrangements; this
methodology is called the “two-step” rearrangement model. Ac-
cording to this model, an atomic rearrangement in a certain
activation volume (step I) initiates the viscous flow of the
surrounding region of volume ⍀ (step II), which leads to a formula
where ␰ is the volume fraction of crystals, a ␰ value of Ͻ10%
would cause an increase in ␩ of Ͻ25%. This finding cannot
sufficiently explain the observed change in ␩. Hence, it is
concluded that the viscosity of the surrounding amorphous matrix
must increase.

3
030
Journal of the American Ceramic Society—Christ et al.
Vol. 83, No. 12
Fig. 10. Measured data and fitted curve of the time-dependent viscosity of the T2-1-derived amorphous ceramic.
for the deformation rate ⑀˙ that can be approximated, in the case of
where ␯ is expected to be approximately the Debye frequency and
0
low stresses, by the relation
Q is the activation energy. In this simple form of the theory, Q is
assumed to be the same for the movement and the formation/
annihilation of flow defects.
␴
kTN ⍀C
0
⑀˙ ͑␴,T,t͒ Ϸ
(7)
t ϩ ␶
The viscosity change, relative to time, is explained by the
annealing out of flow defects, which results in a decrease of the
where ␴ represents the applied stress, ␶ the preannealing time at
the creep-test temperature T, t the creep time, k the Boltzmann
constant, and N0 the volume spectral density of the relaxation
centers. C is a parameter that allows for the orienting effect of the
applied stress on the atomic rearrangements in the relaxation
centers. In this low-stress approximation, ⑀˙ is proportional to ␴.
However, ␩ ϭ ⑀˙ /(3␴); therefore, Eq. (7) can be transformed to
21
amount of free volume. Duine et al. showed that the most-
suitable differential equation that describes the change of the
concentration of free volume C , relative to time, over a large time
f
and temperature range is given by the relation
˙
C ϭ Ϫk C ͑C Ϫ C ͒
(12a)
f
f
f
f
eq
␶
1
where Ceq is the equilibrium flow-defect concentration at the
␩
͑T,t͒ Ϸ
ϩ
ͩ ͪ
t
(8)
testing temperature. If Ceq ϽϽ C , Eq. (12a) can be approximated
3
kTN ⍀C
3kTN ⍀C
f
0
0
as
which indicates that the viscosity is an affine linear function of the
time.
The second model explains the viscosity of amorphous materi-
als using the occurrence of flow defects; this methodology is called
2
f
C˙ ϭ Ϫk C
(12b)
f
f
This equation is a good approximation for the temperature and
time ranges that have been investigated in this work and yields the
solution
1
1,13,20,23
the “free-volume model.”
In this model, atomic transport
for structural rearrangement is caused by flow defects that are
formed by fluctuations in the distribution of the free volume in the
amorphous material. These defects also are available for atomic
transport during deformation. According to this model, the
deformation rate ⑀˙ is given by
Q
2
3
Ϫ1
Ϫ1
Cf ϭ Cf0 ϩ C t exp
ͩ
Ϫ
ͪ
(13)
0
RT
␥0
␯0
␴␥ ␯
0 0
In this equation, C represents the starting value of the concentra-
f
0
⑀˙ ϭ 2C k
sinh ͩ ͪ
(9)
f
f
⍀
2kT
tion of flow defects (C ) and C is a constant.
f 0
In temperature ranges well below the glass-transition tempera-
where C represents the concentration of flow defects, k the jump
f
f
ture, the value of the quantity ␥ V is assumed to be independent
0
0
2
0
frequency of a flow defect, ␥ the shear strain per jump of a single
flow defect, V0 the volume of one defect, and ⍀ the atomic
volume. In the low-stress regime, where the approximation sinh
0
of temperature. The volume of a flow defect (V ) is assumed to
0
be a constant, although V likely decreases under the influence of
0
an external load. Despite these assumptions, there is good corre-
lation between the model and the measured data.
[
␴⑀ V /(2kT)] Ϸ ␴⑀ V /(2kT) is valid, this model predicts the
0 0 0 0
Newtonian viscosity:
Furthermore, the activation energy for the movement of flow
defects in Eq. (11) and the activation energy for the production and
annihilation of flow defects in Eq. (13) are assumed to be equal.
Therefore, in this temperature range, the viscosity according to the
free volume model can be expressed by substituting Eqs. (11) and
kT⍀
␩
ϭ
(10)
2
C k ͑␥ ␯ ͒
f
f
0 0
2
0
According to van den Beukel et al., the jump frequency k is
thermally activated and can be written as
f
(13) into Eq. (10) to derive the following equation:
Q
KT
Q
k ϭ ␯ exp
ͩ
Ϫ
ͪ
(11)
␩͑T,t͒ ϭ
exp
ϩ ͑KC T͒t
(14)
f
0
ͫ ͩ ͪͬ
0
RT
C
RT
f0

December 2000
High-Temperature Mechanical Properties of Si-B-C-N-Precursor-Derived Amorphous Ceramics
3031
where K is a constant, given by
k⍀
K ϭ
(15)
2
͑
␥ ␯ ͒ ␯
0
0
0
Similar to the aforementioned two-step rearrangement model,
the free-volume model also yields an affine linear relation between
the viscosity and the creep or annealing time, respectively. From
this standpoint, both models correlate well with the data shown in
Fig. 10.
(2) Temperature Dependence of the Viscosity
The two-step rearrangement model and the free-volume model
both describe the time dependence of the viscosity data; therefore,
the temperature dependence of ␩ was analyzed according to the
following equation:
␩
͑t,T͒ ϭ a͑T͒ ϩ b͑T͒t
(16)
To measure the temperature dependence of the viscosity, creep
experiments in the temperature range of 1350°–1500°C were
performed. Because of the long test times, the results are plotted in
Fig. 11 on logarithmic scales. The dashed line represents the
expected slope, according to Eq. (16). As expected, this slope is
approached asymptotically at each investigated temperature.
Therefore, Eq. (16) should be valid in the temperature range that
has been investigated here. Although ␩ varies greatly with tem-
perature T for short times, it becomes more independent of
5
temperature at times longer than ϳ3 ϫ 10 s. This observation
Fig. 12. Temperature dependence of the starting viscosity a(T), according
suggests that the a(T) term in Eq. (16) is much more dependent on
temperature than the b(T) term is. To discuss the two deformation
models that have been proposed, it is useful to focus on the starting
viscosity a(T). The a(T) values were obtained by fitting an affine
linear function to the data shown in Fig. 11.
Although the viscosity according to both discussed models is an
affine linear function of the time (Eq. (16)), the models predict
different temperature dependencies of the viscosity. According to
the two-step rearrangement model, a(T) should be proportional to
to (a) the “two-step” relaxation model and (b) the free-volume model.
viscosity is explained better by the free-volume model. An
activation energy for jumps and the annihilation of the flow defects
of Q Ϸ 0.6 MJ/mol was calculated from the slope of the straight
line in Fig. 12(b).
V. Conclusions
1
/T, whereas the free-volume model predicts the following relation
between a(T) and T:
The high-temperature mechanical properties and the oxidation
behavior of Si-B-C-N-precursor-derived amorphous materials
have been studied. During creep testing and annealing treatments
in air, a passivating oxidation layer is formed on the surface of the
material within some hours. Thus, the oxygen-containing atmo-
sphere is not expected to have any significant effect on the
mechanical properties.
Q
a͑T͒ϰT expͩ ͪ
(17)
RT
Consequently, according to the free-volume model, a plot of ln
(a(T)/T) versus 1/T should yield a straight line with the slope Q/R.
Figure 12 shows that the temperature dependence of the starting
Fig. 11. Variation of the viscosity of the T2-1-derived amorphous ceramic, relative to time and temperature. All deformation tests were performed at 50
MPa.

3
032
Journal of the American Ceramic Society—Christ et al.
Vol. 83, No. 12
3
J. Bill and F. Aldinger, “Precursor-Derived Covalent Ceramics,” Adv. Mater., 7,
Only a small volume fraction of crystalline phases can be
7
75–87 (1995).
detected after the annealing experiments. Therefore, one can
conclude that crystallization does not influence the deformation
behavior of the material.
4
(a)H.-P. Baldus and K. Jansen, “Moderne Hochleistungskeramiken—Amorphe
Anorganische, Netzwerke aus Molekularen Vorl a¨ ufern,” Angew. Chem., 109, 338–54
(1997). (b)H.-P. Baldus and K. Jansen, “Novel High Performance Ceramics—
Amorphous Inorganic Networks from Molecular Precursors,” Angew. Chem. Int. Ed.
Engl., 36, 328 (1997).
It has been shown that two components contribute to the
deformation rate of precursor-derived amorphous materials: a
stress-independent shrinkage and a deformation that is propor-
tional to the applied stress. This proportionality suggests that the
deformation mechanism is based on viscous flow (i.e., diffusion).
According to the free-volume model, the shrinkage may be
explained by the reduction of free volume during heat treatment.
The viscosity that is attributed to the stress-dependent deforma-
tion component increases linearly as time increases, and similar
behavior has been observed in metallic glasses. The applicability
of two deformation models that have been developed for this class
of materials has been tested to explain the deformation behavior of
precursor-derived amorphous ceramics; these models are called
the “two-step” rearrangement model and the “free-volume model.”
Both models predict the observed time dependence of the defor-
mation rate and viscosity. However, the free-volume model fits the
observed temperature dependence of the viscosity better than the
two-step rearrangement model does, over the temperature range
that has been investigated. In addition, the density of the pore-free
amorphous ceramic increases after pressureless annealing, because
of the “annealing out” of free volume; thus, this result also
indicates the applicability of the free-volume model.
Both models that have been discussed here predict a linear
relationship of stress versus deformation rate for small-stress
approximations. This observation is in good accordance with the
experimental finding in time range I (see Fig. 5). On the other
hand, slight deviations from the linear behavior are observed in
time range II (see Fig. 6). Further investigations are necessary to
clarify whether the small-stress approximation is still valid in this
range and whether these deviations are caused by some influence
of the applied stress on the viscosity.
5
M. Weinmann, J. Schuhmacher, H. Kummer, S. Prinz, J. Peng, H. J. Seifert, M.
Christ, K. M u¨ ller, J. Bill, and F. Aldinger, “Synthesis and Thermal Behavior of Novel
Si-B-C-N Ceramic Precursors,” Chem. Mater., 12 [3] 623–32 (2000).
6
G. Thurn, J. Canel, J. Bill, and F. Aldinger, “Compression Creep Behavior of
Precursor-derived Si–C–N Ceramics,” J. Eur. Ceram. Soc., 19, 2317–23 (1999).
7
L. An, R. Riedel, C. Konetschny, H.-J. Kleebe, and R. Raj, “Newtonian Viscosity
of Amorphous Silicon Carbonitride at High Temperature,” J. Am. Ceram. Soc., 81 [5]
1
349–52 (1998).
8
B. Baufeld, H. Gu, J. Bill, F. Wakai, and F. Aldinger, “High Temperature
Deformation of Precursor-derived Amorphous Si–B–C–N Ceramics,” J. Eur. Ceram.
Soc., 19, 2797–814 (1999).
9
G. Thurn and F. Aldinger, “Compression Creep Behavior of Precursor-Derived
Ceramics”; pp. 237–45 in Precursor-Derived Ceramics, Proceedings of the Interna-
tional Workshop on Grain Boundary Dynamics of Precursor-Derived Covalent
Ceramics (Schloß Ringberg, 1996). Edited by J. Bill, F. Wakai, and F. Aldinger.
Wiley–VCH Verlagegesellschaft, Weinheim, Germany, 1999.
1
0
R. Riedel, L. M. Ruwisch, L. An, and R. Raj, “Amorphous Silicoboron
Carbonitride Ceramic with Very High Viscosity at Temperatures above 1500°C,”
J. Am. Ceram. Soc., 81 [12] 3341–44 (1998).
1
1
F. Spaepen, “Defects in Amorphous Metals”; pp. 134–74 in Physics of Defects,
Les Houches Lectures XXXV. Edited by R. Balian, M. Kl e´ man, and J.-P. Poirier,
1980.
1
2
A. L. Mulder, S. van der Zwaag, E. Huizer, and A. van den Beukel, “Accurate
Contraction and Creep Measurements During Structural Relaxation of Amorphous
Fe40Ni40B20,” Scr. Metall., 18, 515–19 (1984).
13
M. H. Cohen and D. Turnbull, “Molecular Transport in Liquids and Glasses,”
J. Chem. Phys., 31, 1164–69 (1959).
1
4
A. T. Kosilov, V. A. Mikhailov, V. A. Khonik, and K. Czach, “Kinetics of Creep
in Metallic Glasses,” Phys. Met. Metalloved. (Engl. Transl.), 82 [5] 549–52 (1996).
1
5
A. Kienzle, “Darstellung und Verarbeitung Borhaltiger Elementorganischer
Vorstufen zur Herstellung Keramischer Materialien in den Systemen SiCB und
SiCBN”; Ph.D. Thesis. Universit a¨ t Stuttgart, Stuttgart, Germany, 1994.
16
T. Wichmann; private communications.
1
7
A. Einstein, “Berichtigung zu Meiner Arbeit: ”Eine Neue Bestimmung der
Molek u¨ ldimensionen,“ Ann. Phys. (Leipzig), 34 [4] 591–92 (1911).
1
8
A. I. Taub and F. Spaepen, “The Kinetics of Structural Relaxation of a Metallic
Glass,” Acta Metall., 28, 1781–88 (1980).
1
9
D. Deng, F. Zheng, Y. Xu, G. Qi, and A. S. Argon, “Creep and Structural
Relaxations in Pd40Ni40 20,” Acta Metall. Mater., 41 [4] 1089–107 (1993).
A. van den Beukel, E. Huizer, A. L. Mulder, and S. van den Zwaag, “Change of
Viscosity During Structural Relaxation of Amorphous Fe40Ni40 20,” Acta Metall., 34
3] 483–92 (1986).
Acknowledgments
P
2
0
The authors thank P. Gerstel for the production of the T2-1 polymer and R. Mager
for the preparation of the creep specimens and the technical support.
B
[
2
1
P. A. Duine, J. Sietsma, and A. van den Beukel, “Defect Production and
Annihilation near Equilibrium in Amorphous Pd40Ni40P20 Investigated from Viscos-
References
ity Data,” Acta Metall. Mater., 40 [4] 743–51 (1992).
2
2
1
V. A. Khonik, A. T. Kosilov, V. A. Mikhailov, and V. V. Sviridov, “Isothermal
R. Riedel, A. Kienzle, W. Dreßler, L. M. Ruswisch, J. Bill, and F. Aldinger, “A
Novel Silicoboron Carbonitride Ceramic with Ultra-High Thermal Stability,” Nature
Creep of Metallic Glasses: A New Approach And Its Experimental Verification,”
(
London), 382, 796–98 (1996).
Acta Mater., 46 [10] 3399–408 (1998).
2
23
T. W. Kamphowe, M. Weinmann, J. Bill, and F. Aldinger, “Preparation of
P. de Hey, J. Sietsma, and A. van den Beukel, “Structural Disordering In
Fibre-Reinforced Si-B-C-N Ceramics by Polymer Precursor Infiltration,” Silic. Ind.,
3, 159 (1998).
Amorphous Pd40Ni40
46 [16] 5873–82 (1998).
P20 Induced By High Temperature Deformation,” Acta Mater.,
6
Ⅺ